Image reconstruction using Irradiation

Question

I am a bit confused as to how to go about this.

I have a surface [x,y,z] given by:

[x, y] = meshgrid(-10:10,-10:10);
z = x .* exp(-x.^2 - y.^2);
surf(x, y, z);

I want to use $I=\rho n^TS$ where $\rho=0.1$, $S$ is the sources vector and $n$ is the normal to the surface, to reconstruct the image. Say I want to do this for 10 arbitrary $S$ vectors and reconstruct 10 images. how do I do this?

I tried extracting $n$ by [nx, ny, nz] =surfnorm(x,y,z); but I am confused here as to how to represent the $S$ vector. is it supposed to $2\times 21$? for one vector? Is there an easier way I am missing?

Answer 1

Each point in surface has a normal represented by 3x1 vector so transpose of it is 1x3 . Considering radiance from the source is represented by normal to the source it will be represented by a 3x1 vector.